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Bimodule

In abstract algebra, a bimodule is an abelian group that is both a left and a right module, such that the left and right multiplications are compatible. Besides appearing naturally in many parts of mathematics, bimodules play a clarifying role, in the sense that many of the relationships between left and right modules become simpler when they are…

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Definition

Examples

Further notions and facts

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Map overview Semantic statistics

Bimodule

Nodes42
Edges41
Triples44
Avg. degree1.95
Density0.047619
Components1

How this topic connects Entity context

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Bimodule

Top relations

related to Examples · 29
Bimodule → Addition, Any, EndR, For, However, If, It, Mm, Mn, Note, R-bimodule, R-bimodules, R-EndR, R-module, R-modules, R-R-bimodule, R-S, R-S-bimodule, R-T-bimodule, R-Z-bimodule
related to Further notions and facts · 8
Bimodule → An R-S-bimodule, For, If, R-modules, R-S-bimodules, S-modules, Sop, Using
related to Definition · 5
Bimodule → For, If, R-module, R-S-bimodule, S-module
is a · 2
Bimodule → abelian group, abelian group that is both a left and a right module

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Important terminology

left right ring multiplication bimodules r-module category abelian defined module r-s-bimodule displaystyle r-r-bimodule product homomorphisms also usual natural tensor algebra

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Bimoduleis aabelian group that is both a left and a right module0.90text
Bimoduleis aabelian group0.90text
Bimodulerelated to DefinitionIf0.60section
Bimodulerelated to DefinitionR-S-bimodule0.60section
Bimodulerelated to DefinitionR-module0.60section
Bimodulerelated to DefinitionS-module0.60section
Bimodulerelated to DefinitionFor0.60section
Bimodulerelated to ExamplesFor0.60section
Bimodulerelated to ExamplesMn0.60section
Bimodulerelated to ExamplesR-S-bimodule0.60section
Bimodulerelated to ExamplesMm0.60section
Bimodulerelated to ExamplesAddition0.60section

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    Min side: 3
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